Cream the Butter and Sugars: In a large mixing bowl, beat together the room temperature unsalted butter, light brown sugar, and white granulated sugar until the mixture is light and fluffy. This process should take about 2-3 minutes.
Add Wet Ingredients: Mix in the large egg and vanilla extract, beating until well combined.
Prepare Dry Mixture: In a separate bowl, whisk together the all-purpose flour, baking soda, cream of tartar, and kosher salt.
Combine Mixtures: Gradually add the dry mixture to the wet ingredients, stirring until a thick dough forms.
Shape the Cookies: Scoop out about 1 tablespoon of dough, rolling it into a ball. Roll in cinnamon sugar and place on a baking sheet.
Bake: Preheat the oven to 350°F (175°C) and bake for about 7 minutes or until lightly golden.
Make the Filling: Melt the white chocolate with eggnog and rum, stirring until smooth. Add nutmeg and mix.
Fill the Cookies: Spoon eggnog ganache into the thumbprints of each cooled cookie.
Notes
Optional: Sprinkle a dash of nutmeg on top of the filling for a festive touch.